Problem: Solve for $x$ and $y$ using elimination. ${-6x+4y = -24}$ ${-5x+5y = -5}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-6$ ${-30x+20y = -120}$ $30x-30y = 30$ Add the top and bottom equations together. $-10y = -90$ $\dfrac{-10y}{{-10}} = \dfrac{-90}{{-10}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-6x+4y = -24}\thinspace$ to find $x$ ${-6x + 4}{(9)}{= -24}$ $-6x+36 = -24$ $-6x+36{-36} = -24{-36}$ $-6x = -60$ $\dfrac{-6x}{{-6}} = \dfrac{-60}{{-6}}$ ${x = 10}$ You can also plug ${y = 9}$ into $\thinspace {-5x+5y = -5}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(9)}{= -5}$ ${x = 10}$